Topological modules of continuous homomorphisms

Khan, Liaqat Ali

doi:10.1016/j.jmaa.2008.01.025

Cited by 11 publications

(8 citation statements)

References 26 publications

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“…Definition 9 (cf. [13,14]). Let ( , ) be a commutativenormed algebra, and let ( , ) be a -normed space which is also an -module in the usual algebraic sense.…”

Section: Resultsmentioning

confidence: 99%

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Multipliers of Modules of Continuous Vector-Valued Functions

Khan

Alsulami

2014

Abstract and Applied Analysis

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In 1961, Wang showed that ifAis the commutativeC*-algebraC0(X)withXa locally compact Hausdorff space, thenM(C0(X))≅Cb(X). Later, this type of characterization of multipliers of spaces of continuous scalar-valued functions has also been generalized to algebras and modules of continuous vector-valued functions by several authors. In this paper, we obtain further extension of these results by showing thatHomC0(X,A)(C0(X,E),C0(X,F))≃Cs,b(X,HomA(E,F)),whereEandFarep-normed spaces which are also essential isometric leftA-modules withAbeing a certain commutativeF-algebra, not necessarily locally convex. Our results unify and extend several known results in the literature.

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“…Definition 9 (cf. [13,14]). Let ( , ) be a commutativenormed algebra, and let ( , ) be a -normed space which is also an -module in the usual algebraic sense.…”

Section: Resultsmentioning

confidence: 99%

“…Recall that a left -module is called faithful (or without order) if, for any ∈ , ⋅ = 0 for all ∈ implies that = 0 (cf. [13,14]).…”

Section: Resultsmentioning

confidence: 99%

Multipliers of Modules of Continuous Vector-Valued Functions

Khan

Alsulami

2014

Abstract and Applied Analysis

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“…A proof for the part (i) of this theorem can be found in 16, Theorem 4.3], for the part (ii) see Theorem 3.5 in 16; see also Satz 2.36 in 4. Also for a generalization of this theorem, see 9, 17.…”

Section: \Documentclass{article}\usepackage{amssymb}\begin{document}\mentioning

confidence: 98%

“…The strict topology for Banach modules has been studied extensively by Grosser 4. Recently, Shantha 17 studied the strict topology for locally convex modules and Khan 9 has carried over this study to a non‐locally convex setting; see also 8, 10.…”

Section: Preliminariesmentioning

confidence: 99%

The space of vector‐valued integrable functions under certain locally convex topologies

Maghsoudi

2012

Mathematische Nachrichten

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Let E be a Banach space, Ω a locally compact space, and μ a positive Radon measure on Ω. In this paper, through extending to Lebesgue‐Bochner spaces, we show that the topology β1 introduced by Singh is a type of strict topology. We then investigate various properties of this locally convex topology. In particular, we show that the strong dual of L1(μ, E) can be identified with a Banach space. We also show that the topology β1 is a metrizable, barrelled or bornological space if and only if Ω is compact. Finally, we consider the generalized group algebra \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$L^1(G, \mathbf {A})$\end{document} under certain natural locally convex topologies. As an application of our results, we prove that \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$L^1(G,\mathbf {A})$\end{document} under the topology β1 is a complete semi‐topological algebra.

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“…for more details, see [15]. The strict topology for Banach modules has been studied extensively by Grosser [4]; see also [7][8][9] and [16,17].…”

Section: Introductionmentioning

confidence: 99%

Hypergroup Algebras as Topological Algebras

Maghsoudi

Seoane‐Sepúlveda

2014

Bull. Aust. Math. Soc.

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Let K be a locally compact hypergroup endowed with a left Haar measure and let L 1 (K) be the usual Lebesgue space of K with respect to the left Haar measure. We investigate some properties of L 1 (K) under a locally convex topology β 1 . Among other things, the semireflexivity of (L 1 (K), β 1 ) and of sequentially β 1 -continuous functionals is studied. We also show that (L 1 (K), β 1 ) with the convolution multiplication is always a complete semitopological algebra, whereas it is a topological algebra if and only if K is compact.2010 Mathematics subject classification: primary 43A62; secondary 46A70, 43A20, 46H05.

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Topological modules of continuous homomorphisms

Cited by 11 publications

References 26 publications

Multipliers of Modules of Continuous Vector-Valued Functions

Multipliers of Modules of Continuous Vector-Valued Functions

The space of vector‐valued integrable functions under certain locally convex topologies

Hypergroup Algebras as Topological Algebras

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